Source labels openChecked July 26, 2026

Green's Open Problem 15

Does there exist a Lipschitz function $f : \mathbb{N} \to \mathbb{Z}$ whose graph $\Gamma = \{(n, f(n)) : n \in \mathbb{N}\} \subseteq \mathbb{Z}^2$ is free of 3-term progressions?

Combinatorics AMS 5 AMS 11

Mathematical statement

Does there exist a Lipschitz function $f : \mathbb{N} \to \mathbb{Z}$ whose graph $\Gamma = \{(n, f(n)) : n \in \mathbb{N}\} \subseteq \mathbb{Z}^2$ is free of 3-term progressions?

Statement source: Green's Open Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

green_15

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_15 :    answer(sorry) ↔ ∃ K : ℝ≥0, ∃ f : ℕ → ℤ, LipschitzWith K f ∧      IsAPOfLengthFree {((n, f n) : ℤ × ℤ) | (n : ℕ)} 3 := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Green, Ben. "100 open problems." (2024).background